5 citations · 13 across the 12 of their papers we have counts for
12 papers · 1 filter
Poincaré type inequality for hypersurfaces and rigidity results
Hilário Alencar, Márcio Batista, Gregório Silva Neto
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincaré type inequality. We app…
Rigidity of manifolds admitting stable solutions of an elliptic problem
Marcio Batista, Jose I. Santos
In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitab…
Hardy and Rellich Inequalities for submanifolds in Hadamard spaces
Marcio Batista, Heudson Mirandola, Feliciano Vitorio
Some of the most known integral inequalities are the Sobolev, Hardy and Rellich inequalities in Euclidean spaces. In the context of submanifolds, the Sobolev inequality was proved…
The Caffarelli-Kohn-Nirenberg Inequality for Submanifolds in Riemannian Manifolds
Márcio Batista, Heudson Mirandola, Feliciano Vitório
After works by Michael and Simon [10], Hoffman and Spruck [9], and White [14], the celebrated Sobolev inequality could be extended to submanifolds in a huge class of Riemannian man…
The first Stekloff eigenvalue in weighted Riemannian manifolds
M. Batista, J. I. Santos
In study of eigenvalue problems, a classical problem is the Stekloff eigenvalue problem. There are many estimates of the first non- zero Stekloff eigenvalue, including a sharp esti…
On the first stability eigenvalue of surfaces with constant weighted mean curvature
Márcio Batista, José I. Santos
Let be a compact immersed surface with constant weighted mean curvature in a weighted manifold . In this paper we obtain upper bounds for the first eigenvalue…